1. Field of the Invention
This invention relates generally to the transfer of information by means of an electromagnetic field, and more particularly to the transfer of information by a component of the magnetic vector potential field.
2. Description of the Prior Art
It is known in the prior art to provide systems for the transfer of information utilizing electromagnetic fields which are solutions to Maxwell's equations. These information transfer systems include apparatus for generating modulated electromagnetic fields and apparatus for detecting and demodulating the generated electromagnetic fields. Examples of the prior type information transfer systems include radio and television band-based systems, microwave band-based systems and optical band-based systems.
The Maxwell equations, which govern the prior art transfer of information by electromagnetic fields can be written: ##EQU1## where E is the electric field density, H is the magnetic field intensity, B is the magnetic flux density, D is the electric displacement, J is the current density and .rho. is the charge density. In this notation the bar over a quantity indicates that this is a vector quantity, i.e., a quantity for which a spatial orientation is required for complete specification. The terms CURL and DIV refer to the CURL and DIVERGENCE mathematical operation and can be denoted by the .gradient.x and .gradient.. mathematical operators. The magnetic field intensity and the magnetic flux density are related by the equations B=.mu.H, while the electric field density and the electric displacement are related by the equation D=.epsilon.E. These equations can be used to describe the transmission of electromagnetic radiation through a vacuum or through various media.
It is known in the prior art that solutions to Maxwell's equations can be obtained through the use of electric scalar potential functions and magnetic vector potential functions. The electric scalar potential is given by the expression: ##EQU2## where .phi.(1) is the scalar potential at point 1, .rho.(2) is the charge density at point 2, r.sub.12 is the distance between point 1 and 2, and the integral is taken over all differential volumes. The magnetic vector potential is given by the expression: ##EQU3## where A(1) is the vector potential at point 1, .epsilon..sub.0 is the permittivity of free space, C is the velocity of light, J(2) is the (vector) current density at point 2, r.sub.12 is the distance between point 1 and point 2 and the integral is taken over all differential volumes dv(2). The potential functions are related to Maxwell's equations in the following manner: ##EQU4## where GRAD is the gradient mathematical operation and can be denoted by the .gradient. mathematical operator. ##EQU5## where A can contain, for completeness, a term which is the gradient of a scalar function. In the remaining discussion, the scalar function and the scalar potential function will be taken to be substantially zero. Therefore, attention will be focused on the magnetic vector potential A.
In the prior art literature, consideration has been given to the physical significance of the magnetic vector potential field A. The magnetic vector potential field was, in some instances, believed to be a mathematical artifice, useful in solving problems, but devoid of independent physical significance.
More recently, however, the magnetic vector potential has been shown to be a quantity of independent physical significance. For example, in quantum mechanics, the Schroedinger equation for a (non-relativistic, spinless) particle with charge q and mass m moving in an electromagnetic field is given by ##EQU6## where h is Planchk's constant divided by 2.pi., i is the imaginary number V-1, .phi. is the electric scalar potential experienced by the particle, A is the magnetic scalar potential experienced by the particle and .chi. is the wave function of the particle. The Josephson junction is an example of a device, operating on quantum mechanical principles, that is responsive to the magnetic vector potential.